Representation of thermodynamic properties of ternary systems and its application to the system silver-gold-copper at 1350 K

The article presents a generalized analytical expression for description of the integral excess Gibbs free energy of mixing of a ternary system. Twelve constants of the equation are assessed by the least mean squares regressional analysis of the experimental integral excess data of the constituent binaries; three ternary parameters are evaluated by a regressional analysis based on the partial experimental data of a component of the ternary system. The assessed values of the ternary parameters describe the nature of the ternary interaction in the system. Activities and isoactivities of the components in the Ag-Au-Cu system at 1350 K are calculated and found to be in good agreement with the experimental data. This analytical treatment is particularly useful to ternary systems where the thermodynamic data are available from different sources.

Thermodynamic constraints along isograms in ternary systems: application to three-phase equilibria

Thermodynamic constraints on component chemical potentials in three-phase fields introduced by the various isograms suggested in the literature are derived for a ternary system containing compounds. When compositions of two compounds lie on an isogram, it is associated with specific characteristics which can be used to obtain further understanding of the interplay of thermodynamic factors that determine phase equilibria. When two compounds are shared by adjacent three-phase fields, the constraints are dictated by binary compositions generated by the intersection of a line passing through the shared compounds with the sides of the ternary triangle. Generalized expressions for an arbitrary line through the triangle are presented. These are consistent with special relations obtained along Kohler, Colinet and Jacob isograms. Five axioms are introduced and proved. They provide valuable tools for checking consistency of thermodynamic measurements and for deriving thermodynamic properties from phase diagrams. (C) 1997 Elsevier Science S.A.

Interdiffusion and solid solution strengthening in Ni-Co-Pt and Ni-Co-Fe ternary systems

Diffusion couple experiments are conducted in Co-Ni-Pt system at 1200 degrees C and in Co-Ni-Fe system at 1150 degrees C, by coupling binary alloys with the third element. Uphill diffusion is observed for both Co and Ni in Pt rich corner of the Co-Ni-Pt system, whereas in the Co-Ni-Fe system, it is observed for Co. Main and cross interdiffusion coefficients are calculated at the composition of intersection of two independent diffusion profiles. In both the systems, the main interdiffusion coefficients are positive over the whole composition range and the cross interdiffusion coefficients show both positive and negative values at different regions. Hardness measured by performing the nanoindentations on diffusion couples of both the systems shows the higher values at intermediate compositions.

Interdiffusion and solid solution strengthening in Ni-Co-Pt and Ni-Co-Fe ternary systems

Diffusion couple experiments are conducted in Co-Ni-Pt system at 1200 degrees C and in Co-Ni-Fe system at 1150 degrees C, by coupling binary alloys with the third element. Uphill diffusion is observed for both Co and Ni in Pt rich corner of the Co-Ni-Pt system, whereas in the Co-Ni-Fe system, it is observed for Co. Main and cross interdiffusion coefficients are calculated at the composition of intersection of two independent diffusion profiles. In both the systems, the main interdiffusion coefficients are positive over the whole composition range and the cross interdiffusion coefficients show both positive and negative values at different regions. Hardness measured by performing the nanoindentations on diffusion couples of both the systems shows the higher values at intermediate compositions.

Separation of ternary systems of hydrophilic ionic liquid with miscible organic compounds by RPLC with refractive index detection

A rapid and simple analytical method was developed for the simultaneous and quantitative determination and separation of hydrophilic imidazolium ionic liquids (ILs) (1-butyl-3-methylimidazolium chloride, [C(4)mim]Cl; 1-hexyl-3-methylimidazolium chloride, [C(6)mim]Cl; 1-octyl-3-methylimidazolium chloride, [C(8)mim]Cl; 1-allyl-3-methylimidazolium chloride, [Amim]Cl; or 1-allyl-3-methylimidazolium bromide, [Amim]Br) with miscible ethyl acetate and EtOH and their mixtures using reverse phase liquid chromatography coupled with refractive index detection (RPLC-RI). The influence of 60 to 100% (volume percentage) methanol in the mobile phase on the IL systems ([C(4)mim]Cl, [C(6)mim]Cl, [C(8)mim]Cl, [Amim]Br, or [Amim]Cl)-ethyl acetate-EtOH was investigated.

Phase Equilibria of Binary and Ternary Systems Containing ILs, Dodecane, and Cyclohexanecarboxylic Acid

This paper reports both the binary and ternary phase behavior of ionic liquids for extracting cyclohexanecarboxylic acid (CCA) from dodecane. This system is a model for the extraction of acids representative of naphthenic acids found in crude oils. In order to develop an effective ternary liquid-liquid extraction system the preliminary selection of ionic liquids was based on CCA miscibility and the dodecane immiscibility with selected ILs. A wide range of ILs based on different cations, anions, cation alkyl-chain length, as well as the effect of temperature on the overall fluid phase behavior is reported. Factors such as variation of cation group, anion effect, alkyl-chain length, and temperature all impact the extraction to various degrees. The largest effects were found to be the lipophilicity of the IL cation and the co-ordination ability of the anion. While CCA capacity increased with lipophilicity of the cation, as did the dodecane. Highly coordinating anions such as trifluoroacetate and triflate demonstrated that highly efficient extraction could be obtained producing favorable tie-lines in the ternary phase diagram. Overall, this study demonstrates that ILs can selectively extract acids from hydrocarbon streams and offers possible treatment solutions for problems associated with the processing of high acid crude oils.

Spectrophotometric study of binary and ternary systems involving metal ions and benzylidenepyruvates: Equilibria in aqueous solutions

The protonation of 4-dimethylaminobenzylidenepyruvate (DMBP) and 2-chloro-4-dimethylaminobenzylidenepyruvate (2-CI-DMBP) and their complex formation with Mn(II), Co(II), Ni(II), Cu(II), Zn(II), Pb(II), Cd(II) and Al(III) have been studied by potentiometric and spectrophotometric methods at 25 °C and ionic strength 0.500 M, held with sodium perchlorate. The stability order found for 1 :1 complexes of both ligands is Al(III) > Cu(II) > Pb(II) > Ni(II) > Zn(II) > Co(II) > Cd(II) > Mn(II). The stability changes move in the same direction as the pKa of the ligands. The results are compared with literature values reported for metal ion pyruvate systems. Thermodynamic stabilities of ternary complexes formed in Cu(II)-B-L- systems, where B = 2,2′-bipyridyl (bipy), ethylenediamine or glycinate and L = DMBP or 2-CI-DMBP, were also determined. The Cu(bipy)L+ species are more stable than would be expected on purely statistical grounds. The importance of the :t system associated with bipy on the enhanced stability of its mixed ligand complexes is stressed. Analytical applications of the investigated ligands are outlined.

GE models and algorithms for condensed phase equilibrium data regression in ternary systems: limitations and proposals

Phase equilibrium data regression is an unavoidable task necessary to obtain the appropriate values for any model to be used in separation equipment design for chemical process simulation and optimization. The accuracy of this process depends on different factors such as the experimental data quality, the selected model and the calculation algorithm. The present paper summarizes the results and conclusions achieved in our research on the capabilities and limitations of the existing GE models and about strategies that can be included in the correlation algorithms to improve the convergence and avoid inconsistencies. The NRTL model has been selected as a representative local composition model. New capabilities of this model, but also several relevant limitations, have been identified and some examples of the application of a modified NRTL equation have been discussed. Furthermore, a regression algorithm has been developed that allows for the advisable simultaneous regression of all the condensed phase equilibrium regions that are present in ternary systems at constant T and P. It includes specific strategies designed to avoid some of the pitfalls frequently found in commercial regression tools for phase equilibrium calculations. Most of the proposed strategies are based on the geometrical interpretation of the lowest common tangent plane equilibrium criterion, which allows an unambiguous comprehension of the behavior of the mixtures. The paper aims to show all the work as a whole in order to reveal the necessary efforts that must be devoted to overcome the difficulties that still exist in the phase equilibrium data regression problem.

Correlation of the liquid–liquid equilibrium data for specific ternary systems with one or two partially miscible binary subsystems

This paper presents the results of a liquid–liquid equilibrium data correlation for 11 ternary systems which have not been previously fitted using the NRTL model or, when they have, the results presented in the literature are inconsistent with the experimental behavior of the system. These ternary systems include mixtures with one or two partially miscible pairs. During the correlation process, new restrictions were imposed on the values for the NRTL binary parameters to ensure correct prediction of the total or partial miscibility for the binary pairs involved. In addition, topological concepts related to the Gibbs stability test have been applied in order to validate the results in the whole range of compositions.

Modelling liquid–liquid equilibria for island type ternary systems

Closed miscibility gaps in ternary liquid mixtures, at constant temperature and pressure, are obtained if phase separations occur only in the ternary region, whilst all binary mixtures involved in the system are completely miscible. This type of behaviour, although not very frequent, has been observed for a certain number of systems. Nevertheless, we have found no information about the applicability of the common activity coefficient models, as NRTL and UNIQUAC, for these types of ternary systems. Moreover, any of the island type systems published in the most common liquid–liquid equilibrium data collections, are correlated with any model. In this paper, the applicability of the NRTL equation to model the LLE of island type systems is assessed using topological concepts related to the Gibbs stability test. A first attempt to correlate experimental LLE data for two island type ternary systems is also presented.

Geometrical study of the three-dimensional temperature–composition diagrams. An important aid to understand the behavior of the liquid–vapour equilibrium in ternary systems

In this work the usefulness of qualitatively studying and drawing three-dimensional temperature–composition diagrams for ternary systems is pointed out to understand and interpret the particular behavior of the liquid–vapour equilibrium of non-ideal ternary systems. Several examples have been used in order to highlight the interest and the possibilities of this tool, which should be an interesting support not only for lecturers, but also for researchers interested in experimental equilibrium data determination.

Solubility, Density, Refractive Index, and Viscosity for the Polyhydric Alcohol + CsBr + H2O Ternary Systems at Different Temperatures

The solubility, density, refractive index, and viscosity data for the ethylene glycol + CsBr + H2O, 1,2-propanediol + CsBr + H2O, and glycerin + CsBr + H2O ternary systems have been determined at (288.15, 298.15, and 308.15) K. In all cases, the solubility of CsBr in aqueous solutions was decreased significantly due to the presence of polyhydric alcohol. The liquid–solid equilibrium experimental data were correlated using the NRTL (nonrandom two-liquid) activity coefficient model, considering nondissociation of the dissolved salt in the liquid phase, and new interaction parameters were estimated. The mean deviations between calculated and experimental compositions were low, showing the good descriptive quality and applicability of the NRTL model. The refractive indices, densities, and viscosities for the unsaturated solutions of the three ternary systems have also been measured at three temperatures. Values for all of the properties were correlated with the salt concentrations and proportions of polyhydric alcohol in the solutions.

Energetics of the condensed ternary fuel-oxidizer systems

the heats of reaction of an oxygen-balanced ternary fuel-oxidizer system have been shown to be linearly related to the total oxidizing valences (P0) of the composition. Because calculation of P0 is simple, the method is found to help in evaluating the energetics of such systems. The accuracy of the method when applied to various ternary systems has been discussed.

Modeling of ternary solubilities of solids in supercritical carbon dioxide in the presence of cosolvents or cosolutes

The investigation of ternary solubilities of solids is essential for the efficient design of extraction processes. The ternary solubilities of solids for cosolvent and cosolute systems are complex functions of temperature, pressure and cosolvent/cosolute composition. The intermolecular interactions between the molecules have a significant role in the solubilities of mixed solids in SCCO2 and cosolvent ternary systems. Two model equations were developed for ternary SCCO2 + cosolvent/cosolute systems by using association and activity coefficient models. Both the model equations consist of five adjustable parameters and correlate the ternary solubilities of solids in terms of temperature, pressure, density and cosolvent/cosolute composition. The model equation for cosolvent systems correlated 43 solid pollutants-cosolvent-SCCO2, while the model equation for cosolute systems correlated 19 solute-cosolute-SCCO2 systems available in literature. The average AARD of the model equations are 4.73% and 4.87% for cosolvent ternary systems and mixed solids in SCCO2, respectively. (C) 2011 Elsevier B.V. All rights reserved.